i know the answer is3 liters - i need ot see the work so i can learn how to do the rest of my work!
asked Jan 13, 2015 in Algebra 1 Answers by jennifer

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2 Answers

Let b=the volume of "neat" boric acid in litres. We can write b/(b+3)=7/10 because we added 3 l of water to make a 70% solution (70%=7/10). To find b, cross-multiply to get rid of the fractions: 10b=7b+21, so 3b=21 and b=7 l. What we want know now is how many litres do we have to add to get a 35% solution? Let's call this volume of water v. So b/(b+v)=35/100=7/20. We know b=7, so we can write 7/(7+v)=7/20. Cross-multiply: 140=49+7v. Divide through by 7: 20=7+v, so v=13 l. It appears then we need 13 litres of water to make a 35% solution of boric acid, that's 10 more litres to add to the 3 litres already added, not the 3 l you were expecting.

The only way I can see how the answer might be 6 l (3 l added), is by using proportionality: it takes 3 l of water to make a 70% solution, so to make a 35% solution (half the 70%) we need twice as much water, 6 l, which is an added 3 l. Somehow, though, I don't feel that proportionality is the right approach. I look at this way: instead of 7 litres of pure boric acid, we have 7 red balls. We add 3 balls of water making 10 balls altogether, 7 of which are red. That's 70% red balls. We now add another 10 white balls of water making 20 balls altogether, 7 of which are red. 7 out of 20 is 35%, representing 35% boric acid solution.

Which solution do you think makes the most sense? Discuss with teacher?

answered Jan 14, 2015 by Rod Top Rated User (487,100 points)
I also know the answer is 3 but I don't know how to solve it either.
answered Feb 14 by Dino Zammit Level 3 User (2,720 points)
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